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L. Silnikov, “A Case of the Existence of a Denumerable Set of Periodic Motions,” Soviet Mathematics Doklady, Vol. 6, 1965, pp. 163-166.

has been cited by the following article:

• TITLE: Bifurcation Analysis of Homoclinic Flips at Principal Eigenvalues Resonance

  AUTHORS: Tiansi Zhang, Deming Zhu

  KEYWORDS: Orbit Flip; Inclination Flips; Homoclinic Orbit; Resonance

  JOURNAL NAME: Applied Mathematics, Vol.4 No.2, February 22, 2013

  ABSTRACT: One orbit flip and two inclination flips bifurcation is considered with resonant principal eigenvalues. We introduce a local active coordinate system to establish bifurcation equation and obtain the conditions when the original homoclinic orbit is kept or broken. We also prove the existence and the existence regions of double 1-periodic orbit bifurcation. Moreover, the complicated homoclinic-doubling bifurcations are found and expressed approximately, and are well located.